The Time Machine in this episode is a replica not the original from The Time Machine (1960). The original is owned by film collector Bob Burns who declined the use of it for the show.
During Sheldon's dream, the time machine's display reads "802,701". This is the same year in which Rod Taylor stops in the 1960 movie The Time Machine (1960).
The date on the time machine during Sheldon's (first) dream is April 28, the same date that this episode first aired.
Raj (Kunal Nayyar) said he will match the offer for Leonard (Johnny Galecki)'s collectibles plus a 1000 Rupees and Sheldon (Jim Parsons) asked "What's the exchange rate?". Raj replied "None of your business". 1000 Indian Rupees is approximately 22 USD.
Sheldon mentions that Captain Kirk stole a cloaking device from the Romulans on Stardate 5027.3. He's referring to the the events of The Enterprise Incident (1968).